In my opinion, he's a snake-in-the-grass spineless coward who's word nobody on any side of the aisle dare trust and who lacks an ounce of intellectual or moral integrety beyond self interest. The real problem that Kevin McCarthy has in this political fight for the speakership, is that everybody in both caucuses, has at least one memory of being royally burned, believing that his word and handshake might just something. The man has no character and even among a group historically lacking in that attribute, they expect their leadership to have at least a little buried in his soul. he's a slug leaving a slime trail of broken commitments, everywhere he travels and that makes it real hard to come by that 'majority of members present'. But I could be wrong.
I think you're assessment is correct which is why the pro McCarthy group saying they'll out wait and out last the 20 is an insane tactic. By waiting McCarthy and co dont get what they want whereas the 20 defectors get exactly what they want, him not being speaker. Unless they've got some other back room dealings up their sleeves the Republican party should go with a different candidate after this debacle